## Abstract and Applied Analysis

### Sequential Generalized Transforms on Function Space

#### Abstract

We define two sequential transforms on a function space ${C}_{\mathrm{a,b}}\left[\mathrm{0},T\right]$ induced by generalized Brownian motion process. We then establish the existence of the sequential transforms for functionals in a Banach algebra of functionals on ${C}_{\mathrm{a,b}}\left[\mathrm{0},T\right]$. We also establish that any one of these transforms acts like an inverse transform of the other transform. Finally, we give some remarks about certain relations between our sequential transforms and other well-known transforms on ${C}_{\mathrm{a,b}}\left[\mathrm{0},T\right]$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 565832, 12 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512192

Digital Object Identifier
doi:10.1155/2013/565832

Mathematical Reviews number (MathSciNet)
MR3139459

Zentralblatt MATH identifier
1296.46041

#### Citation

Choi, Jae Gil; Chung, Hyun Soo; Chang, Seung Jun. Sequential Generalized Transforms on Function Space. Abstr. Appl. Anal. 2013 (2013), Article ID 565832, 12 pages. doi:10.1155/2013/565832. https://projecteuclid.org/euclid.aaa/1393512192

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